The doorway in Julie's house is 80 inches tall, and the angle that the diagonal makes with the side of the doorway is 35° as shown in the diagram. Julie has a table top that is 8 feet long. She wants to know if she can move it through the door by leaning it to fit through the door diagonally. What is the length of the diagonal of Julie's doorway to the nearest tenth of an inch?

Question

Mathematics

Catherine Vega

18 January, 17:56

The doorway in Julie's house is 80 inches tall, and the angle that the diagonal makes with the side of the doorway is 35° as shown in the diagram. Julie has a table top that is 8 feet long. She wants to know if she can move it through the door by leaning it to fit through the door diagonally. What is the length of the diagonal of Julie's doorway to the nearest tenth of an inch?

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Answers (1)

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Grace Mckinney · Answer 1

The length of the diagonal will be given by:

cos θ=adjacent/hypotenuse

θ=35°

hypotenuse=h

adjacent=80 inches=6.66667 ft

thus;

cos 35=6.66667/h

h=6.66667/cos35

h=8.1385 ft

diagonal=8.1385 ft

we conclude that the table will through the door diagonally.